GMAT Practice Question: A certain manufacturer sells its product to stores in 113 different regions worldwide, with an...
Question
A certain manufacturer sells its product to stores in 113 different regions worldwide, with an average (arithmetic mean) of 181 stores per region. If last year these stores sold an average of 51,752 units of the manufacturer's product per store, which of the following is closest to the total number of units of the manufacturer's product sold worldwide last year?
- 10^{6}
- 10^{7}
- 10^{8}
- 10^{9}
- 10^{10}
Topics: word problems, calculations, mean, approximations
Solution
Step 1
We identify the number of regions, the average stores per region, and the average units sold per store.
R = 113 S_{\text{avg}} = 181 U_{\text{avg}} = 51752
Step 2
We then calculate the total number of stores by multiplying the number of regions by the average stores per region.
R \times S_{\text{avg}} = 113 \times 181 = 20453
Step 3
We then approximate the total stores and the average units per store in scientific notation for easier multiplication.
20453 \approx 2.0 \times 10^{4} 51752 \approx 5.2 \times 10^{4} 2.0 \times 5.2 = 10.4 10.4 \times 10^{8} = 1.04 \times 10^{9}
Step 4
We compare the estimated value with the powers of ten to find the closest one.
1.04 \times 10^{9} \text{ is closest to } 10^{9}
Answer
10^{9}
